Nash Equilibrium in Higher Education

In a Nash equilibrium, every actor maximizes his utility given the behavior of all the other actors. Arum and Roksa's Academically Adrift contains one of the best (implicit) applications of the concept I've ever read. They name all the key actors involved in higher education - parents, students, professors, administrators, and government funding agencies - and explain why, given the behavior of all the other actors, no one wants to do anything about the problem of "limited learning":

Parents - although somewhat disgruntled about increasing costs - want colleges to provide a safe environment where their children can mature, gain independence, and attain credentials that will help them be successful as adults. Students in general seek to enjoy the benefits of a full collegiate experience that is focused as much on social life as on academic pursuits, while earning high marks in their courses with relatively little investment of effort. Professors are eager to find time to concentrate on their scholarship and professional interests. Administrators have been asked to focus largely on external institutional rankings and the financial bottom line. Government funding agencies are primarily interested in the development of new scientific knowledge.

The next sentence is "In short, the system works." You might be tempted to remind Arum and Roksa that Nash equilibrium and efficiency are totally different things. But their standard of "works" is roughly equivalent to durability:

Limited learning on college campuses is not a crisis because the institutional actors implicated in the system are receiving the organizational outcomes they seek, and therefore neither the institutions themselves nor the system as a whole is in any way challenged or threatened.

Arum and Roksa go on to argue that K-12 education is in some way challenged or threatened. But how hard could it be to extend their Nash analysis to all the key actors in the public school system?

Comments and Sharing

Mmm, I think it's a little incomplete. One, a meaningful number of students want something not listed, i.e., not just a credential but actual marketable skills. I suggest it is employers and graduate schools who want the crdentials ultimately, and see colleges as performing a screening and sorting function. Two, the persons with vesgted interests in student loan and grant programs are not listed. The politicians who sponsor them want votes from the parents, basically.

One problem with this analysis is that there are actually many subgroups of students, professors, etc. One potential route to the university system collapsing is that the subgroup of students with high skills and motivation to learn defects to some other environment. At the moment, universities do have some very good students. If they lose those, even if they are small fraction of the total, the legitimacy of the enterprise would be undermined. It would become more difficult to argue for government support, parents would be less likely to finance study at university, professors would not see as much intellectual benefit from teaching, and less able students would no longer see as much advantage in getting a credential from a university.

Indeed, Tiger Mothers in Seoul and Mumbai are increasingly obsessed with getting their offspring into American colleges, which suggests that from the point of view of an increasingly globalized marketplace, American colleges are doing just fine. Now, as an American parent, you may think that American colleges should try harder to benefit young Americans, but that just shows you are a protectionist, even a nativist, so who cares about you?

The global market for US colleges is not the same as the market for all US colleges. The top 100 can do as they wish -- at least for awhile. The average expensive private school that might not even show up on US News lists is SOL. Ditto for the weakest state schools that need student demand and state subsidies.

I think that it is too much of a generalization to approach it that way.

There are many disciplines where students must learn with maximum effort and universities..
For example, engineering schools have notoriously rigourous course requirements. An the professors in those schools spend a large amount of time on teaching..

I would assume it is also true in other "hard" majors..Sciences, pre-med, architecture, etc.

I think signalling theory needs universities that allow limited learning. If instead of offering easy courses or instead of letting the lazy/uninterested/dumb students fail, they tried to push them to excel or tried to provide a more taylored educational experience to improve their learning, they would tilt the field toward those students and they would be undermining the university role as a signalling device. For the university to be a good signalling device it has to let a lot of their student get a sub-par (or limited) education while allowing the best students to reach their full potential. My view is that in the past 50 years the university has been doing a lot of the signalling work that before was done by highschools, and it is that what I think is very inefficient. The worse the highschool system becomes, the more work the university has to do to sort out a more diverse pool of students.

I would like to add something else. Sometimes I have read in blogs/comments in this site arguments against the 'tenure' system because it breeds lazy professors/researchers, etc. However, under the signalling theory, the main role of professors is not to teach but to judge. In that sense, the 'tenure' system grants them the same conditions to do their work that their peers in the judicial system enjoy. Professor evaluations from students have already undermined the role of grades as a signal in the case of un-tenured professors (can you imagine a defendant accused of murder being able to evaluate his judge, and the judge pay or employment status being linked to those evaluations?) but so far I haven't seen those evaluations affect the other big signal, recommendation letters from tenured professors.

You'll often hear that grad school is the place where students actually learn things they'll need in their jobs. So perhaps colleges will start competing for students by offering more "straight to the master's" programs. These programs would take no or only a little more time, and cost no or only a bit more money, than traditional BA programs. Students would come out with a symbolic BA or BS, and a meaningful master's. To get them through in four or five years, colleges would simply strip out undergraduate electives and all but a few "breadth" requirements.

"Second-tier" schools, hurting for tuition revenue, might be the first to try this system. But I can see it quickly being picked up by other schools - especially state schools under pressure from legislators who want in-state students to get more value for their tuition dollars.

Of course there would still be plenty of four-year liberal arts programs generating grads who need to go to grad school, or work for a few years, to learn job skills. But they could lose a lot of market share to "straight to the master's" programs, because the latter would offer students both better value, and superior signaling power. Grads of both programs would emerge with the requisite pair of diplomas to hang on their office walls. But employers might well see completing a "straight to the master's" program as a signal of greater seriousness than that shown by those with traditional BAs. Perhaps some schools would add on a paying internship at the end of the program, to make graduates even more appealing to employers.

"engineering schools have notoriously rigorous course requirements. An the professors in those schools spend a large amount of time on teaching.."

I graduated as an electrical engineer in 1986 and the coursework I took, except for some basics, is now ridiculously out of date or so esoteric that I never use it. It isn't easy to set up a path of study that maps closely to what you will need in the workforce.

Coming up with a course of study that provides significant value added such that lower quality students will gain a benefit over higher quality students that go to another school is pretty much impossible as far as I can see. Note that schools like University of Chicago and St. Johns try to do something like this in the humanities with increased rigor, but it doesn't particularly seem to help the students.

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